Base Expansion for Nets

Every (ut, um, s)-net N in base b with u ≥ 1 is a (t, m, s)-net in base bu [1, Lemma 2.9].

If N is linear over Fb, the resulting net is also linear over Fb, but in general not over Fbu. Thus the resulting net is in general not digital.

See Also

References

[1]Harald Niederreiter.
Point sets and sequences with small discrepancy.
Monatshefte für Mathematik, 104(4):273–337, December 1987.
doi:10.1007/BF01294651 MR918037 (89c:11120)
[2]Harald Niederreiter.
Constructions of (t, m, s)-nets and (t, s)-sequences.
Finite Fields and Their Applications, 11(3):578–600, August 2005.
doi:10.1016/j.ffa.2005.01.001 MR2158777 (2006c:11090)

Copyright

Copyright © 2004, 2005, 2006, 2007, 2008, 2009, 2010 by Rudolf Schürer and Wolfgang Ch. Schmid.
Cite this as: Rudolf Schürer and Wolfgang Ch. Schmid. “Base Expansion for Nets.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2008-04-04. http://mint.sbg.ac.at/desc_NBExp.html

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